# Sequence Impedance and Network of Power System Elements

To determine the performance or behavior of power system under unbalanced condition it is essential to have knowledge of sequence impedance and networks of power system elements. This is a fundamental knowledge for performing the unsymmetrical fault analysis in power system. Here we will be discussing about the sequence impedance and networks of various power system elements.

## Sequence Impedance and Network of Power System Elements : Synchronous Machine

For determining the sequence impedance and network of power system elements, let us consider an unloaded synchronous machine which can be a generator or motor. It is grounded through a reactor of impedance Zn. Ea, Eb and Ec are the emfs induces in the three phases of the machine respectively.

An unsymmetrical fault on the machine terminals causes unbalanced current Ia, Ib and Ic to flow in the respective phases. If this fault involves the ground then current In flows to neutral from the ground through reactor Zn. The current In is phasor sum of Ia, Ib and Ic.

These unbalanced currents can be resolved into the symmetrical currents and respective positive, negative and zero sequence networks of the machine can be formed.

### Positive Sequence Impedance and Network of Synchronous Machine

Synchronous machines offers time varying reactance Xd”(Sub-transient reactance), Xd‘(transient reactance) and Xd(synchronous reactance).

For a circuit where sudden value of current under switching or fault condition is to be determined, Sub-transient reactance  of the machine is used. To determine the current after the few cycle of switching or fault (3 or 4 cycles), transient reactance Xd‘ is used. For steady-state condition synchronous reactance Xd is used.

Positive sequence impedance along with the reactance of the machine makes up positive sequence sub transient, transient or steady-state impedance of the machine respectively.

Given is the positive sequence network of synchronous machine

The positive sequence impedance of the synchronous machine is represented by a source emf on no load and the positive sequence impedance of the machine. The phasor sum of positive sequence currents of the three phases Ia1, Ib1, Ic1 are zero, so no current flows through neutral and Zn doesn’t appear in the network.

### Negative Sequence Impedance and Network of Synchronous Machine

Negative sequence reactance X2 of the synchronous machine oscillates between the direct axis reactance Xd”and quadrature axis reactance Xq”. X2 value is usually taken average and given by ### Zero Sequence Impedance and Network of Synchronous Machine

The current flowing in the neutral through reactor impedance Zn is sum of the zero sequence currents in all three phases. So, the voltage drop caused by these sum of zero sequence current is 3Ia0Zn. The voltage drop of zero sequence terminal is 3Ia0Zn + Ia0Zg0. The zero sequence impedance is given by Zg0. Zero sequence network of transmission line is shown below.

Zero sequence voltage of terminal ‘a’ is ## Sequence Impedance and Network of Power System Elements: Transmission Line

For a transmission line positive and negative sequence impedance are equal. Zero sequence impedance includes the impedance of the return path through the ground is different from positive and negative sequence impedance. Zero sequence impedance of transmission line is much larger than the positive and negative sequence impedance.

For a fully transposed transmission line there is no mutual coupling between the sequence networks.

## Sequence Impedance and Network of Loads

A star-connected load with isolated neutral has no path for flow of zero sequence current. It offers infinite impedance between the neutral and ground leaving behind the zero sequence network open circuited between the neutral of the star connected load and the reference bus.

When neutral of the star connected load is grounded through a reactor of impedance Zn then zero sequence voltage drop will occur due to flow of zero sequence current through Zn given by 3Ia0 Zn. This is same as that of Ia0 flowing through 3Zn. So, an impedance of 3Zn is introduced between the neutral terminal and the reference bus of the zero sequence network as shown.

For a balanced load the positive, negative and the zero sequence impedance of the load is equal.

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